Question

A Cycle Was Sold At A Gain Of $10\%$. Had It Been Sold For $₹260$More, The Gain Would Have Been $14\%$. Find The Cost Price Of The Cycle.

Answer 1

Finding the cost price :

Let$x$ be the cost price of the cycle

Given, Selling price when the cycle is sold at a gain of $14\%$

$$\begin{gathered} =\frac{(100+G\%)}{100}\times C.P. \\ =\frac{(100+14)}{100}\times x \\ =\frac{114x}{100} \end{gathered}$$

Selling price when cycle is sold at gain of $10\%$

$$\begin{gathered} =\frac{(100+10)}{100}\times x \\ =\frac{110x}{100} \end{gathered}$$

Difference in S.P.$=₹260$

$\begin{array}{rcl}\frac{114x}{100}-\frac{110x}{100}& =& 260\\ \frac{4x}{100}& =& 260\\ x& =& \frac{260\times 100}{4}\\ x& =& 6500\end{array}$

Therefore, the cost price of the cycle is $Rs.6500$.